快速排序法02:普通快速排序法的优化

随机化选择标定点

为了解决对有序数组排序,快速排序法复杂度变成O(n^2)的问题,在partition()方法中随机化选择一个元素作为标定点

import java.util.Arrays;
import java.util.Random;

public class Algorithm {

    public static void main(String[] args) {

        Integer[] arr = {3, 2, 5, 1, 0};
        QuickSort.sortOptimized(arr);

        System.out.println(Arrays.toString(arr));
    }
}

class QuickSort {

    private QuickSort(){}

    public static<E extends Comparable<E>> void sortOptimized(E[] arr){

        /**
         * 将重复使用的temp和random变量作为参数传递,进行内存优化
         */
        Random random = new Random();
        E temp = null;
        sortOptimized(arr, 0, arr.length - 1, random, temp);
    }

    public static<E extends Comparable<E>> void sortOptimized(E[] arr, int left, int right, Random random, E temp){

        if (left >= right){
            return;
        }

        int p = partition(arr, left, right, random, temp);

        sortOptimized(arr, left, p - 1, random, temp);
        sortOptimized(arr, p + 1, right, random, temp);
    }

    public static <E extends Comparable<E>> int partition(E[] arr, int left, int right, Random random, E temp){

        /**
         * 生成[left, right]之间的随机索引,然后和left互换位置作为第一个元素
         * random.nextInt()方法只能生成[0, bound)的整数,而分区间是以left起始的,长度为right - left + 1,所以在left的基础上,再生成[0, right - left + 1)范围内的整数
         */
        int p = random.nextInt(right - left + 1) + left;

        temp = arr[p];
        arr[p] = arr[left];
        arr[left] = temp;

        int j = left;

        for (int i = left + 1; i <= right; i++) {

            if (arr[i].compareTo(arr[left]) < 0){

                j++;
                temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
            }
        }

        temp = arr[j];
        arr[j] = arr[left];
        arr[left] = temp;

        return j;
    }
}

练习:对于总是将中间的元素作为标定点的快速排序,编写一个算例,生成一个中间元素总是最小的数组,即让这个快速排序法“失效”

import java.util.Arrays;
import java.util.Random;

public class Algorithm {

    public static void main(String[] args) {

        Integer[] testScale = {10000, 100000};

        for (Integer n : testScale) {

            Integer[] randomArr = ArrayGenerator.generatorRandomArray(n, n);
            Integer[] sortedArr = ArrayGenerator.generatorSortedArray(n);
            Integer[] specialArr = ArrayGenerator.generateSpecialArray(n);

            Integer[] arr1 = Arrays.copyOf(randomArr, randomArr.length);
            Integer[] arr3 = Arrays.copyOf(randomArr, randomArr.length);

            Integer[] arr2 = Arrays.copyOf(sortedArr, sortedArr.length);
            Integer[] arr4 = Arrays.copyOf(sortedArr, sortedArr.length);

            Integer[] arr5 = Arrays.copyOf(specialArr, specialArr.length);
            Integer[] arr6 = Arrays.copyOf(specialArr, specialArr.length);

            System.out.println("测试随机数组排序性能");
            System.out.println();

            Verify.testTime("QuickSortMid", arr1);
            Verify.testTime("QuickSortOptimized", arr3);

            System.out.println();

            System.out.println("测试有序数组排序性能");
            System.out.println();

            Verify.testTime("QuickSortMid", arr2);
            Verify.testTime("QuickSortOptimized", arr4);

            System.out.println();

            System.out.println("测试特殊数组排序性能");
            System.out.println();

            Verify.testTime("QuickSortMid", arr5);
            Verify.testTime("QuickSortOptimized", arr6);

            System.out.println();
        }
    }
}

class QuickSort {

    private QuickSort(){}

    public static<E extends Comparable<E>> void sortMid(E[] arr){

        E temp = null;
        sortMid(arr, 0, arr.length - 1, temp);
    }

    public static<E extends Comparable<E>> void sortMid(E[] arr, int left, int right, E temp){

        if (left >= right){

            return;
        }

        int p = partition(arr, left, right, temp);

        sortMid(arr, left, p - 1, temp);
        sortMid(arr, p + 1, right, temp);
    }

    public static <E extends Comparable<E>> int partition(E[] arr, int left, int right, E temp){

        int mid = left + (right - left) / 2;

        temp = arr[mid];
        arr[mid] = arr[left];
        arr[left] = temp;

        int j = left;

        for (int i = left + 1; i <= right; i++) {

            if (arr[i].compareTo(arr[left]) < 0){

                j++;
                temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
            }
        }

        temp = arr[j];
        arr[j] = arr[left];
        arr[left] = temp;

        return j;
    }

    public static<E extends Comparable<E>> void sortOptimized(E[] arr){

        Random random = new Random();
        E temp = null;
        sortOptimized(arr, 0, arr.length - 1, random, temp);
    }

    public static<E extends Comparable<E>> void sortOptimized(E[] arr, int left, int right, Random random, E temp){

        if (left >= right){

            return;
        }

        int p = partitionOptimized(arr, left, right, random, temp);

        sortOptimized(arr, left, p - 1, random, temp);
        sortOptimized(arr, p + 1, right, random, temp);
    }

    public static <E extends Comparable<E>> int partitionOptimized(E[] arr, int left, int right, Random random, E temp){

        int p = random.nextInt(right - left + 1) + left;

        temp = arr[p];
        arr[p] = arr[left];
        arr[left] = temp;

        int j = left;

        for (int i = left + 1; i <= right; i++) {

            if (arr[i].compareTo(arr[left]) < 0){

                j++;
                temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
            }
        }

        temp = arr[j];
        arr[j] = arr[left];
        arr[left] = temp;

        return j;
    }
}

class ArrayGenerator {

    private ArrayGenerator() {}

    public static Integer[] generatorRandomArray(Integer n, Integer maxBound) {

        Integer[] arr = new Integer[n];
        Random random = new Random();

        for (int i = 0; i < n; i++) {
            arr[i] = random.nextInt(maxBound);
        }

        return arr;
    }

    public static Integer[] generatorSortedArray(Integer n) {

        Integer[] arr = new Integer[n];

        for (int i = 0; i < n; i++) {
            arr[i] = i;
        }

        return arr;
    }

    public static Integer[] generateSpecialArray(int n) {

        Integer[] arr = new Integer[n];
        generateSpecialArray(arr, 0, n - 1, 0);

        return arr;
    }

    public static void generateSpecialArray(Integer[] arr, int left, int right, int value) {

        if (left >= right) {

            return;
        }

        int mid = left + (right - left) / 2;

        /**
         * 生成中间值总是最小的数组,就是反向模拟partition()这个过程
         * partition()过程是将中间值和第一个元素互换,我们的目的是让这个中间值最小,这样换了以后,下一个左区间没有元素,每次只能将第一个最小的元素排好序
         * 反向模拟,就是先让数组的中间元素最小,然后和第一个元素互换,再对剩下的[left + 1, right]区间进行同样的递归
         */
        arr[mid] = value;
        int temp;
        temp = arr[mid];
        arr[mid] = arr[left];
        arr[left] = temp;

        generateSpecialArray(arr, left + 1, right, value + 1);

        temp = arr[mid];
        arr[mid] = arr[left];
        arr[left] = temp;

        /**
         * 因为mid是左区间最后一个元素,因此左区间的元素都会被赋值,可是右区间最后一个元素可能不会被递归到,因为mid的取值是向下取整
         * 为了防止最后一个元素没有被赋值,所以要额外判断一下,如果没有遍历到,可以赋值一个大于value的值
         */
        if (arr[right] == null){
            arr[right] = value + 2;
        }
    }
}

class Verify {

    private Verify (){}

    public static<E extends Comparable<E>> boolean isSorted(E[] arr){

        for (int i = 0; i < arr.length - 1; i++) {

            if (arr[i].compareTo(arr[i + 1]) > 0) {

                return false;
            }
        }

        return true;
    }

    public static<E extends Comparable<E>> void testTime(String AlgorithmName, E[] arr) {

        long startTime = System.nanoTime();

        if (AlgorithmName.equals("QuickSortMid")) {
            QuickSort.sortMid(arr);
        }

        if (AlgorithmName.equals("QuickSortOptimized")) {
            QuickSort.sortOptimized(arr);
        }

        long endTime = System.nanoTime();

        if (!Verify.isSorted(arr)){
            throw new RuntimeException(AlgorithmName + "算法排序失败!");
        }

        System.out.println(String.format("%s算法,测试用例为%d,执行时间:%f秒", AlgorithmName, arr.length, (endTime - startTime) / 1000000000.0));
    }
}

普通快速排序法还有问题

在目前的partition()方法,数组的元素越无序,快速排序法的性能越好。虽然随机化选择标定点对有序的数组也有了性能的提升

但还有一个问题:如果数组的所有元素都一样,那就等价于是完全有序数组,而且随机化标定点的策略也会失效,此时快速排序法的复杂度仍会降到O(n^2)

posted @ 2021-10-23 11:29  振袖秋枫问红叶  阅读(65)  评论(0)    收藏  举报